Simplify the following expression: $\dfrac{64q^4}{72q^2}$ You can assume $q \neq 0$.
Solution: $ \dfrac{64q^4}{72q^2} = \dfrac{64}{72} \cdot \dfrac{q^4}{q^2} $ To simplify $\frac{64}{72}$ , find the greatest common factor (GCD) of $64$ and $72$ $64 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(64, 72) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{64}{72} \cdot \dfrac{q^4}{q^2} = \dfrac{8 \cdot 8}{8 \cdot 9} \cdot \dfrac{q^4}{q^2} $ $\phantom{ \dfrac{64}{72} \cdot \dfrac{4}{2}} = \dfrac{8}{9} \cdot \dfrac{q^4}{q^2} $ $ \dfrac{q^4}{q^2} = \dfrac{q \cdot q \cdot q \cdot q}{q \cdot q} = q^2 $ $ \dfrac{8}{9} \cdot q^2 = \dfrac{8q^2}{9} $